Fuenmayor is a Spanish surname. Notable people with the surname include:
Denisse Fuenmayor (born 1979), Venezuelan softball player Johana Fuenmayor, Venezuelan fencer Juan Fuenmayor (born 1979), Venezuelan footballer Manuel Fuenmayor (born 1980), Venezuelan javelin thrower Ruy Fernández de Fuenmayor (1603–1651), Spanish soldier and colonial governor